Inverse problems for locally perturbed lattices -- Discrete Hamiltonian and quantum graph
Mathematical Physics
2022-02-03 v1 math.MP
Spectral Theory
Abstract
We consider the inverse scattering problems for two types of Schr\"odinger operators on locally perturbed periodic lattices. For the discrete Hamiltonian, the knowledge of the S-matrix for all energies determines the graph structure and the coefficients of the Hamiltonian. For locally perturbed equilateral metric graphs, the knowledge of the S-matrix for all energies determines the graph structure.
Keywords
Cite
@article{arxiv.2202.00944,
title = {Inverse problems for locally perturbed lattices -- Discrete Hamiltonian and quantum graph},
author = {Emilia Blåsten and Pavel Exner and Hiroshi Isozaki and Matti Lassas and Jinpeng Lu},
journal= {arXiv preprint arXiv:2202.00944},
year = {2022}
}
Comments
36 pages, 4 figures